The present invention relates to electromagnetic induction well logging. More specifically, the present invention relates to an improved method of focusing the measurements obtained with array induction tools in a deviated borehole.
The production of hydrocarbons from subsurface formations typically commences by forming a borehole through the earth to a subsurface reservoir thought to contain hydrocarbons. From the borehole, various physical, chemical, and mechanical properties are xe2x80x9cloggedxe2x80x9d for the purpose of determining the nature and characteristics, including for example, the porosity, permeability, saturation, and depth, of the subsurface formations encountered. One such logging technique commonly used in the industry is referred to as induction logging. Induction logging measures the conductivity or its inverse, the resistivity, of a formation. Formation conductivity is one possible indicator of the presence or absence of a significant accumulation of hydrocarbons because, generally speaking, hydrocarbons are relatively poor conductors of electricity. Formation water, on the other hand, typically salty, is a relatively good conductor of electricity. Thus, induction logging tools can obtain information that, properly interpreted, indicates the presence or absence of hydrocarbons.
These induction (also known as electromagnetic induction) well logging instruments were first introduced by Doll, H. G., xe2x80x9cIntroduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud,xe2x80x9d Journal of Petroleum Technology, June, 1949, pp. 148-62. Induction well logging instruments typically include a sonde having one or more transmitter coils and one or more receiver coils at axially spaced apart locations. Induction well logging instruments also typically include a source of alternating current (AC) which is conducted through the transmitter coils. The AC passing through the transmitter coils induces a magnetic field within the surrounding formation, causing the flow of eddy currents within the earth formations. In general, the magnitude of the eddy currents is proportional to the electrical conductivity (the inverse of the electrical resistivity) of the earth formations surrounding the instrument. The eddy currents, in turn, induce a magnetic field that is coupled to the receiver coil, thereby inducing in the receiver coil a voltage signal with magnitude and phase dependent upon the electrical characteristics of the adjacent formation.
Typically, the signal from the receiver coil is applied to one or more phase detection circuits, each of which generates a signal proportional to the magnitude of that component of the receiver coil signal having a particular, predetermined phase. Thus, one such phase detector circuit senses the magnitude of the component of the receiver coil signal that is in-phase with the transmitter current in the transmitter coil. This component signal is commonly referred to as the real or inphase (R) component. A second phase detection circuit commonly used in induction logging tools detects the component of the receiver coil signal that is 90xc2x0 out of phase with the transmitter current.
This latter component signal is commonly referred to as the quadrature-phase (X) component signal. Because the output signal from the receiver coil is not itself an absolute measure of conductivity, but rather is merely proportional to the true formation conductivity, the output signal must be processed to obtain a log or plot of the true formation conductivity as a function of axial depth in the borehole. Most modem theoretical analysis of induction log processing is based upon the work of H. G. Doll which is summarized in his 1949 article. According to Doll""s analysis, the in-phase component of the signal induced in the receiver coil is directly proportional to the conductivity of the surrounding formation, and the constant of proportionality, referred to by Doll as the xe2x80x9cgeometrical factor,xe2x80x9d is a function of the geometry of the tool as it relates to the portion of the formation being measured.
Doll calculated what he termed the xe2x80x9cunit geometrical factor,xe2x80x9d which defines the relationship between the conductivity of a so-called xe2x80x9cunit ground loop,xe2x80x9d a horizontal loop of homogeneous formational material having a circular shape with its center on the axis of the borehole and having a very small, square cross section, and the elementary voltage signal contributed by the unit ground loop to the total in-phase signal induced in the receiver coil. By integrating the unit geometrical factor across all unit ground loops lying within a horizontal plane spaced at some axial distance z from the center of the coil system, Doll obtained the geometrical factor for a xe2x80x9cunit bed.xe2x80x9d A plot of this geometrical factor as a function of the axial distance from the center of the coil system gives what is commonly referred to as the xe2x80x9cvertical geometrical factorxe2x80x9d for the tool. It is an accurate plot of the sonde response function relating formation conductivity to output voltage measurements for the tool, assuming no attenuation or phase shift of the induced magnetic field as a consequence of the conductivity of the surrounding formation.
Induction logging technology has evolved significantly since its introduction by Doll. In recent years, induction devices consisting of several complex coil combinations have been replaced by tools with multiple arrays (see, for example, Beard, D. R., et at., xe2x80x9cA New, Fully Digital, Full-spectrum Induction Device for Determining Accurate Resistivity with Enhanced Diagnostics and Data Integrity Verification,xe2x80x9d SPWLA 37th Annual Logging Symposium, June, 1996, Paper B; Beard, D. R., et at., xe2x80x9cPractical Applications of a New Multichannel and Fully Digital Spectrum Induction System,xe2x80x9d SPE Annual Technical Conference and Exhibition, 1996, Paper No. 36504; and Barber, T. D., et at., xe2x80x9cA Multiarray Induction Tool optimized for Efficient Wellsite Operation,xe2x80x9d SPE 7oth Annual Technical Conference and Exhibition, 1995, Paper No. 30583). Each array consists of one transmitter and a pair of receiver coils. These new induction devices are commonly referred to as array-type induction tools.
A simple induction array (two-coil array and three-coil array) responds to all its surrounding media, including formations, the borehole, and invasion zones if there are any. This response will be degraded by severe borehole effect and will suffer from low vertical and radial resolution. In order to avoid the weaknesses of the simple induction arrays, array combinations are used to increase the response contribution from the medium of interest, such as uninvaded formation, and at the same time to reduce the response contribution from the medium of disinterest, such as the borehole. This process by which the output of an induction logging instrument is made to effectively zoom in on a specific space of its surrounding medium and mute the unwanted peripherals is referred to as focusing.
The older style tools attempt to focus the tool response using carefully selected coil arrangements. The focusing therefore is fixed by the tool design, i.e. these tools are xe2x80x9chardware-focusedxe2x80x9d. In array-type induction tools, the measurements from various arrays are combined through a software algorithm to achieve focusing of the signal response, i.e. these tools are xe2x80x9csoftware-focusedxe2x80x9d. This processing produces a set of curves with predetermined depth of investigation, vertical resolution and other optimized 2-D features.
Using software-based focusing provides greater flexibility for handling various logging environments and for creating more reliable induction logs. However, the quality and accuracy of the final focused logs are dependant on the accuracy of the software focusing method.
Prior art focusing methods are based on a method that was proposed by Barber and Zhou (see Barber, T. D. and Rosthal, R. A., xe2x80x9cUsing a Multiarray Induction Tool to Achieve High-Resolution Logs with Minimum Environmental Effects,xe2x80x9d SPE 66th Annual Technical Conference and Exhibition, 1991, Paper No. 22725 and Zhou, Q., Beard, D. and Tabrovsky L., xe2x80x9cNumerical Focusing of Induction Logging Measurements,xe2x80x9d 12th Workshop in Electromagnetic Induction in Earth,xe2x80x9d August, 1994) and is, for reference purposes, here referred to as the xe2x80x9cconventional focusing methodxe2x80x9d. The conventional focusing method can be expressed mathematically as                                           σ            TRF                    ⁡                      (            z            )                          =                              ∑                          i              =              1                                      m              ary                                ⁢                                    ∑                                                z                  xe2x80x2                                =                                  z                  min                                                            z                max                                      ⁢                                                            W                  i                                ⁡                                  (                                      z                    xe2x80x2                                    )                                            ⁢                                                σ                  ai                                ⁡                                  (                                      z                    -                                          z                      xe2x80x2                                                        )                                                                                        (        1        )            
where "sgr"ai is the measured log from the ith array; Wi is the focusing filter; mary is the total number of arrays; and zmin and zmax define the depth window surrounding the output point.
Theoretically, the software focusing method described by eq. (1) can be traced back to the Born approximation (a linear approximation of the measured response of a medium) and then the condition for eq. (1) is an assumption of an homogeneous background. This focusing method produces good quality focused logs when the formation conductivity varies with small to moderate contrasts between adjacent formation beds. However, when the formation conductivity varies with very large conductivity contrasts, i.e. if the formation is very xe2x80x9cinhomogeneousxe2x80x9d, the focused logs are not as good as would be expected.
The root cause of this shortcoming is the nonlinearity of the induction response with respect to the formation conductivity. The basic assumption for the focusing algorithm expressed through eq. (1) is that the array measurements behave linearly with conductivity. The error due to the violation of this linearity assumption is referred to as the nonlinearity effect. The nonlinearity effect is formation-dependent: the larger the inhomogeneity, the stronger the nonlinearity effect. A focusing method based on a formation response with a homogeneous background, propagates or even amplifies the nonlinearity effect.
In a given logging environment, the inhomogeneity of a formation is described by numerous factors. Formation layering contributes to the vertical inhomogeneity, which is conventionally described by the Rt/Rs contrast, where Rt is the formation resistivity and Rs is the shoulder resistivity. Radial inhomogeneity is expressed through the Rt/Rx0 and the Rx0/Rm contrast, where Rx0 is the resistivity of the invaded zone and Rm is the mud resistivity. Other inhomogeneities are introduced through borehole irregularity, tool eccentricity, borehole deviation, etc. Despite the multitude of factors, the vertical inhomogeneity often dominates, particularly when the Rt/ Rs contrast is large.
The induction logging response function varies with formation inhomogeneity due to the nonlinearity of the induction measurements. The focusing filters are designed based on Born geometric factors, which equal the response functions under a homogeneous background. With such designed filters and eq. (1), the nonlinearity effect is propagated or even amplified through the focusing process, especially when the formation is inhomogeneous with a large conductivity contrast.
U.S. patent application Ser. No. 09/264,105 (now U.S. Pat. No. 6,219,619) having the same assignee as the present application and the contents of which are fully incorporated herein by reference, teaches use of an an inhomogeneous background formation model. Using this inhomogeneous background formation model, the formation response of the induction tool measurement can be split into two portions: the response due to an inhomogeneous background conductivity, a background response, and a certain xe2x80x9cresponse residuexe2x80x9d. The background response is the computer simulated measurements of the inhomogeneous background model. The response residue is the difference between raw measurements and the background responses.
The ""105 application uses an initial formation model estimated from raw array measurements or processed logs and used as the background conductivity model. For the background response, the focusing result can be directly obtained using focusing target functions instead of applying the conventional focusing processing. Therefore, the focusing result of the background response is ideal and free of any nonlinearity effect. The conventional focusing procedure is applied to the response residue. The final focusing response is obtained by adding the two focusing results. Due to the relatively small amplitude of the response residue, the nonlinearity effect introduced to the focused result is very small. Hence, the nonlinearity effect on the final focusing result is largely reduced. Thus, by introducing an inhomogeneous formation background model into the focusing algorithm, an improved focusing method is achieved having a reduction in the propagation of nonlinearity effects.
The teachings of the ""105 application are, however, limited to near vertical wells (wells in which the borehole axis makes a small angle with the normal to the bedding planes). In highly deviated wells when the angle between the normal to the bedding planes and wellbore axis is large, array induction measurements exhibit erratic spikes, misleading curve separations, and inaccurate resistivity values, preventing log analysts from accurately evaluating invasion and formation resistivities. There is a need for a method of determination of formation resistivities in deviated boreholes. Such a method should preferably also account for any anisotropy in the resistivity of the formations. The present invention satisfies this need.
The present invention is a method and apparatus of using an induction logging tool in a deviated borehole within earth formations for determining an anisotropic conductivity of the formation. An anisotropic background model is estimated from borehole corrected data. An asymptotic conductivity of the anisotropic background model is determined based on the horizontal and vertical conductivities of the model and a known inclination of the tool to the normal to the bedding planes. A modeled response is calculated for this anisotropic background model using a forward modeling program and skin effect corrections are applied to this modeled response. A response residual is calculated as a difference between the skin-effect corrected response and the borehole corrected data. This residual is focused and focused residual is combined with a focused output of the background model. Where appropriate, the intermediate outputs are converted to a true vertical depth to account for the inclination of the borehole axis.